Wildlife Trade ad Edagered Specie rotectio aul C. Miio Departmet of Ecoomic Ryero Uiverity Toroto, ON Caada, M5B2K3 Jue 23, 2004 Abtract Market for edagered pecie potetially geerate icetive for bot legal upply ad poacig. To deter poacig, govermet ca ped o eforcemet or icreae legal arvetig to reduce te retur from poacig. A leader-follower commitmet game i developed to examie tee coice i te preece of illegal arvetig ad te reultig impact o pecie tock. I additio, curret trade retrictio impoed uder CITES are examied. Wit Courot coecture amog poacer, te model detail te ubgame perfect equilibrium iteractio betwee poacig level, eforcemet ad legal arvetig. JE Claificatio: Q2, F13, Q28, C72 Keyword: wildlife trade, edagered pecie, eforcemet, deterrece, limited etry. --------------------------- Ti reearc wa upported i part by te Social Sciece ad Humaitie Reearc Coucil of Caada (SSHRC) Doctoral Fellowip #752-97-1609. Te autor i grateful for te commet of Jo Mulle, two aoymou referee, Ida Ferrara, Carle lourde, Sam Bucovetky, Elie Appelbaum ad Jim Brox, ad emiar participat at Wilfrid aurier Uiverity, te Uiverity of Maitoba, Waigto College, akeead Uiverity, te Uiverity of Sakatcewa, ad te 1999 Caadia Ecoomic Aociatio meetig (Toroto). Ay error remai te repoibility of te autor. Telepoe: (416) 979-5000 x6186; Fax: (416) 979-5289; E-mail: pmiio@ryero.ca 0
1 Itroductio ad Backgroud Wile abitat detructio ad traformatio a bee coidered te leadig factor i edagerig pecie, everal ig-profile extictio ave bee te direct reult of overarvetig, ad may oter curretly edagered pecie are ubect to arvetig for iteratioal trade. CITES, te Covetio o Iteratioal Trade i Edagered Specie of Wild Faua ad Flora, wa eacted i Marc 1973 i a attempt to eure tat pecie do ot become extict a a reult of uc arvetig. Uder te Covetio, pecie lited i Appedix I (uc a te giat pada, tiger, ad Autralia dugog) are ubect to complete ba o iteratioal trade, wile toe i Appedix II (icludig te bottle-oed dolpi, wale ark, ad black pider mokey) ted to ave le evere retrictio o trade, icludig quota o arvet ad cutom requiremet. Wile te actual utig or gaterig of pecie may be relatively imple ad ubect to ope-acce, te poacig of edagered pecie for ale i foreig market i potetially limited to toe wit te reource ad coectio to traport ad ell plat or aimal iteratioally witout beig eaily caugt (likely more o for trade i live aimal). Ti implie tat previou model of wildlife maagemet, predomiatly caracterized by eiter perfect competitio or a igle uer (moopoly), do ot alway accurately portray te realitie of wildlife poacig. Imperfect competitio amog poacer, were idividual poacer ave ome impact o price, would be a more appropriate modelig coice for may pecie market. Te ue of game teory allow te iteractio betwee poacer to be explicitly modeled i order to better decribe ow tee aget will repod to te actio of teir competitor poacer ad to te arvetig ad eforcemet deciio of te govermet. Specifically, quatity (or Courot) competitio amog poacer i employed i ti paper, were eac 1
poacer idepedetly elect teir ow arvet ad tat arvet iteract wit te legally actioed arvet ad te arvet of oter poacer troug te price of te good, ad ca alo be affected by eforcemet troug te expected puimet of beig caugt. Hece, ti paper examie two ditict policy optio available to cocered govermet of coutrie wit arveted edagered pecie. Te firt i to ue pyical or moetary reource for protected area, guard, pecial cutom officer, ad te like, i order to icreae te probability of catcig illegal arveter, tereby icreaig te expected fie/puimet for poacig. Te ecod deterrece metod i to actio te proviio of pecie to te market, drivig dow te price ad terefore te retur to poacig. Modelig te coice of te legal arvet of te govermet imultaeouly wit te arvet coice of poacer would reult i a market caracterized by perfect competitio (ule te legal cot ad beefit are ubtatially differet from toe of poacer). Te govermet would be a igle producer amog may, eac witout te capacity to igificatly affect te price. Deterrece troug iger legal arvet would terefore ot be poible a te price received by poacer would ot cage. If te govermet were itead able to commit to particular arvet ad eforcemet level prior to te deciio of poacer, te govermet could ave a impact o toe deciio ad be i a poitio to actively limit (ome) poacig wit it wildlife maagemet policy. For ti purpoe, te govermet coice of arvet (or dometic legal quota if direct cotrol i ot poible) ad eforcemet i ere coidered a te firt move i a two-tage o-cooperative game wit poacer. 1 Agai, wile certai pecie market may be better uited to a competitive ope-acce caracterizatio (uc a may 1 Te iteratioal oil market ca be tougt of i te ame way, wit te OEC cartel ettig it ow oil productio for a period ad oter mall producig coutrie te cooig teir ow productio level. Te key differece ere i tat bot te firt ad ecod mover elect pecie from te ame tock. 2
commoly coumed fi pecie), may edagered pecie or teir part caot imply be take acro a earby border ad old to a ed-uer but mut be traported over log ditace to coutrie wit trict import regulatio, ad accordigly, teir market ca more appropriately be modeled wit a limited umber of arveter (or limited etry). Autralia, for example, i a maor (legal) et exporter of crocodile ki ad importer of wild orcid (World Reource Ititute, 2000), a well a avig burgeoig illegal market for macaw, palm cockatoo, ad oter bird. Ope-acce wit illegal activity a received muc more attetio i te reource maagemet literature, begiig wit Adero ad ee (1986), ad Millima (1986), ad more recetly, Bulte ad va Koote (1999), Burto (1999), Alexader (2000) ad Kremer ad Morcom (2000). imited etry wit illegal activity a alo bee previouly aalyzed by Sutie ad Adere (1985) ad Crabbé ad og (1993). Bot of tee paper abtract from pricig dyamic ad focu o arvet deciio. I ti paper, te goal i to imultaeouly determie te eforcemet level, legal arvetig ad poacig we poacer ave ome degree of market power. oacer act accordig to Courot coecture (o tere i o trategic collaboratio), ad cooe teir illegal arvet after te govermet a et te legal arvet quatity or quota. I te cotext of te propoed framework, te impact of te CITES policie o welfare, poacig, eforcemet ad edagered pecie tock i explicitly evaluated. For example, particular trade ba, uc a te 1989 elepat ba, ca be examied. 2 Te remaider of te paper decribe te ubgame perfect Na equilibria of te two- 2 Africa rage tate ave ow mixed reult after te ba, altoug may ave oberved overall icreae i elepat populatio depite populatio preure, civil war, abitat detructio, ad local killig i repoe to crop-raidig. Some atio, icludig Cameroo, Malawi, ad Tazaia, ave experieced lower etimated poacig after te ba, wile oter, uc a Keya ad Zimbabwe, ave iger pot-ba poacig etimate, depite te fact tat eforcemet i term of moetary expediture i all five of tee atio ave decreaed (1989 etimate from Barbier et al. (1990); 1995 (o-peculative) etimate from Said et al. (1995)). 3
tage game. Backward iductio, begiig wit poacig ad workig back to te govermet coice, i ued to olve te game. I te ecod tage, detailed i ectio 2, te idividual poacer cooe teir arvet level give te legal arvet ad eforcemet level et by te govermet. I ectio 3 ad 4, te govermet cooe te legal arvet ad eforcemet level uder a pure profit obective (ectio 3) ad a profit-ad-tock obective (ectio 4), accoutig for ow idividual ad total poacig are affected by it deciio. 2 Idividual ad Total oacig Coice imited etry i modeled troug a fixed ad fiite umber of rik-eutral poacer,, wit idetical cot. If we let be te arvet of poacer, uig te upercript to differetiate poacig from te legal arvet, ad be te tock, te cot of arvetig (wic i tockdepedet) will be c ( ), wit c 0 ad c 0. oacer are aumed to cotribute otig to te protectio of abitat to maitai te pecie tock. Te arvet of all poacer oter ta poacer, deoted, ca be writte i (1) i A i te above metioed tudie, te market for legal ad illegal product i te ame: tere i a igle demad curve for te product i quetio, idepedetly of te metod by wic it i provided. A repreetative poacer maximize expected idividual profit, give te legal arvet ad te govermet eforcemet level e a determied by te firt tage (ad tu cotat for te purpoe of poacig coice), ad te arvet of all oter poacer,. Te expected idividual profit, or te differece betwee poacig reveue ad te cot related to arvetig ad (expected) puimet, are 4
p E( ) p( ) c( ) ( e) ( ) (2) were i te fial tock level, wic i equal to it iitial value le te um of te total arvet of poacer ad te legal arvet, or ( ), p( ) p( ) i te demad fuctio wit p 0 ad p 0, i te puimet fuctio (exogeou ad covex), ad (e) i te eforcemet tecology, wit 0 ad 0, tat i te probability of catcig a poacer i icreaig i te govermet-coe level of eforcemet wit o-icreaig retur. poacer Te profit-maximizig coditio, wic yield te reactio fuctio (, ) of, i p p c c 0 (3) Hece, poacer arvet util te beefit from arvetig oe additioal uit (te price received from output) equal te um of te margial cot of arvetig tat uit, te icreae i te expected fie ad te profit lot troug te reultig decreae i te price of output. Aumig a ymmetric Courot equilibrium amog poacer (a i Crabbé ad og), te reactio fuctio for total poacig i p were te total arvet by all poacer i p c c ( e) 0 (4) (5) by ymmetry. Te reactio fuctio (4) ow ow total poacig i affected by te firt-tage govermet coice variable, te legal arvet ( ) ad eforcemet level ( e ). Te particular reactio to tee variable are provided below. Rearragig (4), total poacig arvet ca be 5
writte a c p p c (6) or tat eac poacer receive a price for eac arveted uit (p) greater ta te um of te cot ad expected puimet from te lat uit ( c ), a te deomiator i egative. For poacig to ot occur, te price aociated wit te optimizig legal arvet would te ave to be lower ta te um of te expected cot ad puimet aociated wit te firt uit poaced. Ti could occur if (a) legal arvetig a a igificat cot advatage o tat te legal arvet i large ad te market price coequetly low, or (b) eforcemet i ufficietly ig or effective o tat te expected puimet i ig relative to te price. Returig to te poacig coice ad te poacig reactio fuctio, we ca oberve (by total differetiatio of (6)) tat te reactio of total poacig to legal arvet level, ceteri paribu, i R d d p p p p p c c c c c 0 (7) wic i trictly egative. 3 Higer legal arvet ifluece poacig i everal way, te mot importat beig te price effect troug te demad fuctio ad cot effect troug te tockdepedecy of te poacig cot fuctio. Furter, we kow tat total poacig decreae by le ta oe uit we legal arvetig icreae by oe uit, or 4 3 p '' Te ecod order coditio for poacig (divided by ) i c p - c - 0, o tat (we combied wit p <0 ad c <0) te deomiator i egative. I additio, te umerator i poitive ice te lope of margial reveue i le (or equal to) ta te lope of te demad curve (wic implie - p p 0 ) ad c >0. 4 I ti cae, te umerator i a ubet of te deomiator. Te additioal term i te deomiator all ave te ame reiforcig ig (egative), makig te deomiator a larger egative umber. Ti implie tat te etire R mut be a fractio, ece te abolute value i le ta oe. 6
0 R 1 (8) Ti follow from two elemet: tat idividual firm ca collectively exercie ome (poibly mall but poitive) degree of market power, ad tat eforcemet i effective, a R e d de p p p c c c 0 (9) A decreae i legal offtake would te provide a price icetive to expad poacig output, but at te ame time, eforcemet impoe a cot o poacig additioal uit. Wit a covex puimet fuctio, te margial expected puimet may be quite ig. Eforcemet effect partially offet price effect, ad a a reult, poacig will icreae but ot by te full cage i te legal arvet. For a give umber of poacer ad iitial tock, te reactio fuctio for total poacig i dowward lopig i bot eforcemet ad legal arvet, o eforcemet ad legal arvet are poacig deterret. I electig te legal arvet ( ) ad eforcemet level (e) to maximize it obective, te govermet mut take ito accout tee reactio of total poacig. Accordigly, we move to te firt tage of te game, icorporatig te reactio fuctio (4) ito te govermet obective, weter ti be to maximize te retur from te legal arvet (te followig ectio) or wit bot te legal arvet ad te tock level (ectio 4). 3 Stock-Idepedet Reource Maagemet For te purpoe of ti ectio, we aume tat te govermet maximize te legal et retur from te maagemet of te tock: tat i, te reveue from legal arvetig ale ad expected fie, le te cot of abitat protectio ad arvetig. Ti may be te cae we cotrol over arvetig i made by a reource maager cocered oly wit te direct retur from te tock, ad erve a a becmark for te followig ectio, were welfare alo deped o tock 7
maagemet. 5 To allow for differece i te cot tructure betwee te (idetical) poacer ad te legal arveter, let te legal arvet cot fuctio be d ) (. I additio to productio cot, we aume tat tere i a opportuity cot of lad, o tat iger tock level require additioal abitat ad take lad from alterative ue. Te cot of abitat protectio ( icluive of opportuity cot of lad) required to utai a particular tock level i aumed to l(), be icreaig i te tock at a icreaig rate ( l 0 ad l 0 ). ad cot erve to decreae coervatio icetive, weter te reource maager i cocered wit te tock level or ot. We coider te govermet to ave eiter direct cotrol over arvetig or idirect cotrol over te ditributio of idividual quota wic um to te total legal arvet latter beig coitet wit Appedix II of CITES. Wit quota, ditributive effect are igored, o tat te govermet may freely ditribute or carge a fee for te quota ad te legal arvetig ector become paive i te ee tat legal arvet coice of idividual firm are give by te ditributio of quota. Eforcemet capital, e, i purcaed o a competitive, te iteratioal market at a parametric price r 1. Te total expected retur from te tock i te te differece betwee te reveue from te legal arvet ad fie applied to caugt poacer ad te cot of arvetig, eforcemet ad lad protectio Maximizatio of (10) wit repect to E( ) p d l( ) e e (10) (iterior) legal take of pecie, give by, wit R from (7) take ito accout, yield te p p R d R l d d p lr R (11) 5 Oter govermet obective, icludig acievig a particular tock level by ellig liceig fee ad balacig teir budget, are ditict poibilitie but are outide te cope of ti paper. 8
Optimal eforcemet expediture i foud by maximizig (10) wit repect to e, wit R e from (9) take ito accout, wic yield p R e d R e e e 1 R lr (12) Tee two coditio (11) ad (12) ca be iterpreted i a relatively traigtforward maer. Te margial beefit of arvetig, or te left-ad-ide of (11), i compried of te direct additioal reveue from ellig te lat uit at te market price (p) ad te idirect additioal reveue derived from (i) te decreae i total arvetig cot due to tock effect (d ) ad (ii) te icreae i te price (p), eac geerated by te egative relatioip betwee legal arvetig ad te level of total poacig (tat i, troug R ), ad (iii) te reductio i te abitat protectio cot (l) a a iger arvet implie a lower remaiig tock to coerve. Te margial cot of arvetig, te rigt-ad-ide of (11), i compoed of te direct additioal cot of arvetig te lat uit (d), te idirect cot of te lot reveue o all uit old at a lower price due to a iger arvet (p ), te effect o total arvetig cot from arvetig more (d ), te additioal abitat protectio cot (l) ad te expected lo i puimet reveue ( R ) from te coequet reductio i poacig (agai, troug R ). Similarly, te left-ad-ide of (12) i te margial beefit of eforcemet, wic coit of a iger price of (ad reveue from) te arveted good (p ), a lower uit arvetig cot (d, from lower poacig troug R e ), ad a iger probability of catcig poacer ad tu iger expected fie ( ). Te rigt-ad-ide of (12) i te margial cot of eforcemet, wic coit of te expediture itelf, te expected lot fie reveue ( ), ad te iger abitat protectio required (l) from le poacig (agai troug R e ). From (11), te legal arvet may be zero ad oly poacig may occur we, amog oter factor, abitat protectio i particularly expeive or legal arvetig cot are 9
proibitively ig, poacig i igificatly more efficiet, or poacig level are ig (o tat te price i low relative to cot, a i potetially te cae we te umber of poacer,, i large). To illutrate te relatioip betwee legal ad poacig arvet, coider te example provided i Figure 1 to 3. 6 Figure 1 ow te legal arvet ad total poacig uder differet umber of poacer i te market. A te umber of poacer icreae, tere i little cage i te legal arvet but poacig icreae, aymptotically covergig to te legal arvet (o tat te total of legal ad poacig arvet i trictly icreaig i te umber of poacer). At low umber of poacer (), idividual poacer utilize teir (o-colluive) market power to tradeoff uit poaced for iger product price. However, a competitio icreae amog poacer, ti trade-off diappear ad te reactio of total poacig to legal arvetig approace egative oe (tat i, if poacig wa perfectly competitive, a decreae i legal arvetig by oe uit would icreae poacig by te ame amout accordig to (7)), ad eforcemet become le effective from (9). 7 Noetele, te firt-move of te govermet i electig a particular legal arvet level prior to poacer electig teir ow arvet eure a legal arvet tat i iger ta total poacig for ay fiite umber of poacer. Figure 2 ow te ame ituatio but wit poacer avig a cot advatage over legal arveter, uc a we arvetig cot are te ame but te govermet icur igificat abitat protectio cot. Here, te lower arvetig cot may allow poacer to overcome te firt-mover advatage of legal arveter ad ear iger profit a poacig level ca exceed legal arvet. 6 Te example provided i for illutrative purpoe oly. See Appedix A for detail. All of te cocluio ad iferece tat follow are geeral ad tu ot retricted to te example i quetio. artial output ad eforcemet level are permitted for implicity. 7 Eforcemet become le effective ere becaue te mall idividual poacer arvet uder competitio reduce te expected puimet more ta proportioally due to te covexity of te puimet fuctio. If te expected puimet wa liear i te poacig level, tere would be o cage i te effectivee of eforcemet. 10
Ba o legal arvetig ca be implemeted uder agreemet uc a CITES, or ca be uilaterally eforced by importig or exportig coutrie. I te cotext of te model, uppoe iitially tat te relatioip betwee te probability of catcig poacer ad illegal arvet remai te ame after te implemetatio of a ba. A ba o legal arvetig will limit to zero, promotig poacig troug te (iger) price of output. However, to acertai te overall impact o poacig, we mut examie te impact o eforcemet a well. Uder a ba, poacer collectively arvet to atify (4), a previouly. Te relatioip betwee ad e (tat i, e R ) remai egative ad ucaged from (8), ad te govermet imply maximize te et expected retur eared from eforcemet le abitat protectio cot, or Eforcemet i tu coe accordig to E( ) ( e) ( ) e l( ) (13) e e 1 R lr (14) wic differ from it couterpart (12) i tat it exclude te beefit of a iger price of te arveted good (p) ad lower lad protectio cot ( l ). Tu, for te ame poacig arvet, eforcemet a a maller margial beefit ad ucaged margial cot, ad tu would decreae after a ba. However, te icreaed poacig aociated wit te reductio i legal arvetig icreae te margial beefit of eforcemet ad decreae it margial cot, puig eforcemet upward. Tee two oppoite effect geerate two poibilitie. If te reactio of total poacig coice to te legal arvet ( R ) i relatively large, bot poacig ad eforcemet could icreae a a reult of a trade ba. Coverely, we eforcemet i igly effective ad legal arvet cage ave mall effect o poacig coice ( e R i low, uc a we te umber of poacer i mall), eforcemet icreae ad te poacig arvet 11
decreae. Bot cae, owever, would reult i iger tock level ta before te ba (. I eac cae, total poacig, i geeral, i le ta te um of legal ad illegal arvetig tat reult i te abece of a ba, ad, a uc, trade ba ca be aid to be more coervative ta we permittig legal arvetig. Oce a ba i itituted, owever, illegal product caot eter coutrie i te guie of legal good, ad a ba may terefore ave te effect of icreaig te probability of catcig poacer, eve if eforcemet ad poacig level do ot cage, ay from (e) to (e), were ( x) ( x) ad ( x) ( x) for all x 0. I oter word, te eacemet of te eforcemet tecology may erve to rotate te probability fuctio upward. I ti cae, a ba would ave te additioal poitive effect of icreaig eforcemet effectivee, a te reactio of total poacig to eforcemet become ˆ e e R R 0 p c p p c c (15) At te ame time, te margial cot of eforcemet icreae (due to fewer fie ad iger abitat protectio cot), ad ti implie le eforcemet effort. Hece, two coflictig effect o total poacig eue: a lower eforcemet level (e) but more effective eforcemet (a iger e R ). It i terefore poible tat poacig fall, eve wit lower eforcemet, a log a te cage i te probability of catcig poacer i ufficietly large. 4 Dometic ad Exteral Coervatio Beefit We a govermet take ito accout tat private idividual may old o-ue value or pecie may provide idirect beefit ot captured i trade market (above lad ue cot), te lower arvet level aociated wit trade retrictio may make tem preferred over te free 12
market. 8 I uc a cae, te poacig reactio fuctio i ucaged from (4), but te govermet maximize a oit obective uc a U ( E( ), ) (16) wic i aumed, for implicity, to be additively eparable ad quai-liear i expected profit, or equivaletly tat te margial utility of profit i uaffected by te tock level. Te ocial value fuctio ca te be writte U E( ) v( ) (17) were i te cotat, poitive weigt placed o expected profit, ad v 0 ad v 0, or tere i poitive but dimiiig margial utility from te tock level. Give tat poacer react to teir arvet ad eforcemet level accordig to (7) ad (9), repectively, te legal arvet i coe accordig to p p v 1 R d d 1 R l [1 R ] R 1 R 0 (18) ad eforcemet accordig to e e e e v e p R d R lr R 1 R 0 (19) Compared to te profit-maximizig coice of te previou ectio, te variatio ere i geerated by (i) te additioal margial cot of arvetig i (18) i te amout of te utility lot from icreaed arvetig ad te reultig tock decreae, v, et of te effect of te reultig reductio i poacig (tat i, troug R ) ad (ii) te utility gai from eforcemet i (19), geerated by reduced poacig (tat i, troug R e ). Te preece of te tock i te obective fuctio tu erve to decreae legal arvetig ad icreae eforcemet. Wile te former 8 Te market ere, except for eforcemet, i uregulated i te ee tat o taxe or oter meaure ca be 13
icreae poacig, te latter ted to decreae it. Te overall effect te deped o tee relative cage, o tat poacig icreae if eforcemet i particularly ieffective (implyig tat te cage i te margial cot wit a ba i mall). Ay icreae i te level of total poacig doe ot exceed te reductio i legal arvetig, ad te tock level i iger relative to tat uder pure profit maximizatio, a illutrated i Figure 3. Eve wit idetical cot, ti implie tat poacig may well exceed te legal arvet, depedig o te umber of poacer (), a te govermet reduce it ow arvet to eure a iger tock level depite te reultig iger poacig arvet. Wit a trade ba, optimal eforcemet i uc tat e e v e R lr 1 R 0 (20) wic differ agai from te profit-maximizig cae i tat tere i a additioal beefit derived from te larger tock a poacig fall. Ti would imply tat eforcemet would be iger ta wit a ba ad o exitece value. ower poacig would reult a well. Alteratively, ad potetially more importatly, we may coider a ituatio i wic exitece value for a pecie are ot eld by local idividual but by toe i oter coutrie, a i te cae we dometic idividual ave more urget cocer ta te urvival of a particular eigborig pecie (iger demad for evirometal ameitie i ofte aociated wit icreaig icome). Uder CITES, deciio regardig pecie are made durig te biaual Covetio of artie, i wic te maority of member repreet coutrie oter ta toe cotaiig te pecie temelve. A perual of reervatio toward pecie' litig (obectio to a particular claificatio or trade retrictio) ow tat mot are made by ot coutrie. Te quetio te arie a to weter a ba o arvetig i uperior to te employed to correct te market failure. 14
mimaagemet of te profit-maximizig reource maager: a ba a te beefit of a iger tock level, but te profit from legal arvetig are abet. Wit o coideratio for profit a ba would prevail, but te deciio of CITES are baed o bot profit ad tock level. A ba i oly preferable i ti ceario we margial exitece value (v) are ig, equilibrium fie per uit are ig ad eforcemet i quite effective, o tat poacig doe ot ubtatially icreae wit a ba, reducig te tock o muc tat lot profit are ot offet. 5 Cocluio Ti paper attempt to formalize te iteractio betwee poacig, eforcemet, ad legal arvetig. I doig o, te limited etry, illegal activity literature i exteded by edogeizig all tree of tee variable. I ituatio were poacig i ot perfectly competitive, commitmet to legal arvet ad eforcemet level i aticipatio of poacig ca erve to reduce poacig, ad i cae of eiter igly effective ad efficiet eforcemet or of a igificat legal arvetig cot advatage poibly elimiate poacig altogeter. Hig opportuity cot for lad, owever, would igificatly reduce te likeliood of ti occurrig, o tat partial deterrece of poacig by legal arvet would likely reult. Depedig o te ature of te demad for te product derived from te pecie, te cot of arvetig ad te effectivee of eforcemet, te model decribed ere illutrate tat legal arvetig may i fact be more effective at reducig poacig level ta iger eforcemet expediture. Ti i certaily ot alway be te cae, but a pre-commitmet to legal arvetig doe reduce poacig i geeral. Te reactio fuctio for total poacig i dowward lopig i bot te legal arvet ad eforcemet. Wit repect to legal arvetig, te lope of te reactio fuctio i greater ta egative oe, o tat decreae i legal arvet are oly partially offet by icreae i 15
poacig. Optimal legal arvet may be zero we abitat protectio cot are ig, poacig a a igificat cot advatage, or te umber of poacer i ig. I geeral, owever, a combiatio of legal arvet ad eforcemet expediture yield iger retur ta eforcemet aloe. I order to regulate trade i edagered pecie, CITES a typically employed trade ba ad arvet quota. We a govermet (or reource maager) imply maximize te ret received from legal arvet, a trade ba (or zero legal arvet) uambiguouly reduce profit. If te reactio fuctio of poacig i teep (poacig i quite eitive to te legal arvet), bot poacig ad eforcemet icreae a a reult of a ba. If itead eforcemet i igly effective ad legal arvet do ot ave large impact o total poacig (uc a we te umber of poacer i mall), a ba ca reult i iger eforcemet ad lower poacig. I ay cae, te poitive effectivee of eforcemet expediture o poacig level lead to iger pecie tock level wit ba, a te icreae i poacig doe ot completely offet te reduced legal arvet. Ti iger tock level make a ba more appealig we a govermet i cocered wit te tock level a well a te retur from legal activity ta uder a profit-maximizig obective. 6 Appedix A A umerical example wa ued to create Figure 1 to 3. Te coice of parameter value wa arbitrary ad wa meat to illutrate te teoretical reult. To ti ed, a liear ivere demad curve of te form A b( H H ), a tock-depedet cot fuctio c( ) k( 0 ) / 0, a 1/ 2 cocave probability fuctio a(e), ad a expoetial puimet fuctio g( H / ) 2 were ued, wit A b, a, k, ad g beig pecified parameter. Idividual ad total poacig arvet were foud a a fuctio of te govermet coice variable, ad 16
coequetly te legal arvet wa foud to maximize te legal obective ubect to te idividual ad total poacig reactio fuctio. For te Figure, te fixed umber of poacer wa varied to demotrate te variou potetial outcome uder differet degree of poacig competitio. 7 Referece Alexader, Robert R. (2000) ``Modellig Specie Extictio: Te Cae for No-Coumptive Value.'' Ecological Ecoomic 35(2): 259-69. Adero, ee G., ad Dwigt R. ee (1986), ``Optimal Goverig Itrumet, Operatio evel ad Eforcemet i Natural Reource Maagemet: Te Cae of te Fiery,'' America Joural of Agricultural Ecoomic 68, 678-690. Barbier, Edward B., Joae C. Burge, Timoty Swao, ad David W. earce, Elepat, Ecoomic ad Ivory (Eartca ublicatio td.: odo, 1990). Bare, R. F. W., G. C. Craig, H. T. Dubli, G. Overto, W. Simo, ad C. R. Toule, Africa Elepat Databae (Cambridge: Black Bear re td., 1999). Bulte, Erwi H., ad G. Coreli va Koote (1999), ``Ecoomic of Atipoacig Eforcemet ad te Ivory Trade Ba.'' America Joural of Agricultural Ecoomic 81(May): 453-66. Burto, Micael (1999), ``A Aemet of Alterative Metod of Etimatig te Effect of te Ivory Ba o oacig Effort.'' Ecological Ecoomic 30(1): 93-106. Crabbé, illipe, ad Ngo Va og (1993), ``Etry Deterrece ad Overexploitatio of te Fiery,'' Joural of Ecoomic Dyamic ad Cotrol 17, 679-704. Kremer, Micael, ad Carle Morcom (2000) ``Elepat.'' America Ecoomic Review 98(1): 212-34. Millima, Scott R. (1986), ``Optimal Fiery Maagemet i te reece of Illegal Activity,'' Joural of Evirometal Ecoomic ad Maagemet 13, 363-381. Said, M. Y., R. N. Cuge, G. C. Craig, C. R. Toule, R. F. W. Bare, ad H. T. Dubli, Africa Elepat Databae 1995 (IUCN: Glad, Switzerlad, 1995). Sutie, Jo G., ad eder Adere (1985), ``Te Ecoomic of Fierie aw Eforcemet,'' ad Ecoomic 61(4), 387-397. 17
World Reource Ititute, World Reource 2000-2001 (Oxford Uiverity re, Oxford, 2000). 18
18 16 14 Harvet () 12 egal oacig 10 8 6 0 10 20 30 40 50 60 70 80 90 100 Number of oacer () Figure 1. egal ad poacig arvet wit pure-retur obective ad idetical cot (idetical arvetig cot but poitive govermet abitat protectio cot). 30 25 20 Harvet () 15 egal oacig 10 5 0 0 5 10 15 20 25 30 35 40 45 50 Number of oacer () Figure 2. egal ad poacig arvet wit pure-retur obective ad a cot advatage to poacer. 19
979 977 Stock evel () 975 973 971 rofit Oly Stock+rofit 969 967 0 2 4 6 8 10 12 14 16 18 20 Number of oacer () Figure 3. Stock level uder pure profit ad tock-ad-retur obective 20